# Python: Merge sort

## Python Search and Sorting: Exercise-8 with Solution

Write a Python program to sort a list of elements using the merge sort algorithm.

Note: According to Wikipedia "Merge sort (also commonly spelled mergesort) is an O (n log n) comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output."

**Algorithm:**

Conceptually, a merge sort works as follows :

- Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
- Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.

An example of merge sort:

**Merge Sort: Pictorial Presentation**

**Sample Solution**:

**Python Code:**

```
def mergeSort(nlist):
print("Splitting ",nlist)
if len(nlist)>1:
mid = len(nlist)//2
lefthalf = nlist[:mid]
righthalf = nlist[mid:]
mergeSort(lefthalf)
mergeSort(righthalf)
i=j=k=0
while i < len(lefthalf) and j < len(righthalf):
if lefthalf[i] < righthalf[j]:
nlist[k]=lefthalf[i]
i=i+1
else:
nlist[k]=righthalf[j]
j=j+1
k=k+1
while i < len(lefthalf):
nlist[k]=lefthalf[i]
i=i+1
k=k+1
while j < len(righthalf):
nlist[k]=righthalf[j]
j=j+1
k=k+1
print("Merging ",nlist)
nlist = [14,46,43,27,57,41,45,21,70]
mergeSort(nlist)
print(nlist)
```

Sample Output:

Splitting [14, 46, 43, 27, 57, 41, 45, 21, 70] Splitting [14, 46, 43, 27] Splitting [14, 46] Splitting [14] Merging [14] Splitting [46] ------- Merging [14, 21, 27, 41, 43, 45, 46, 57, 70] [14, 21, 27, 41, 43, 45, 46, 57, 70]

**Flowchart: **

**Python Code Editor :**

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